Classification of gigapixel Whole Slide Images (WSIs) is an important prediction task in the emerging area of computational pathology. There has been a surge of research in deep learning models for WSI classification with clinical applications such as cancer detection or prediction of molecular mutations from WSIs. Most methods require expensive and labor-intensive manual annotations by expert pathologists. Weakly supervised Multiple Instance Learning (MIL) methods have recently demonstrated excellent performance; however, they still require large slide-level labeled training datasets that need a careful inspection of each slide by an expert pathologist. In this work, we propose a fully unsupervised WSI classification algorithm based on mutual transformer learning. Instances from gigapixel WSI (i.e., image patches) are transformed into a latent space and then inverse-transformed to the original space. Using the transformation loss, pseudo-labels are generated and cleaned using a transformer label-cleaner. The proposed transformer-based pseudo-label generation and cleaning modules mutually train each other iteratively in an unsupervised manner. A discriminative learning mechanism is introduced to improve normal versus cancerous instance labeling. In addition to unsupervised classification, we demonstrate the effectiveness of the proposed framework for weak supervision for cancer subtype classification as downstream analysis. Extensive experiments on four publicly available datasets show excellent performance compared to the state-of-the-art methods. We intend to make the source code of our algorithm publicly available soon.